Question

Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a...

Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)

B(x) is “x is a ball.”

R(x) is “x is round.”

S(x) is “x is a soccer ball.”

  1. All soccer balls are round. ______________________
  2. Some balls are soccer balls.____________________
  3. There exists a ball that is not a soccer ball._________________
  4. Every ball is round.___________________________
Math   Advanced-Math   
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Answer #1

EXPLANATION:

(a) "All soccer balls are round." can be restated as "For every object x in the world, if x is a soccer ball then x is round."

(b) "Some balls are soccer balls." can be restated as "For some object x in the world, if x is a ball then x is a soccer ball."

(c) "There exists a ball that is not a soccer ball." can be restated as "There exists an object x in the world such that x is a ball and x is not a soccer ball."

(d) "Every ball is round." can be restated as "For every object x in the world, if x is a ball then x is round."

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